Arescue plane flies horizontally at a constant speed searching for a disabled boat. when the plane is directly above the boat, the boat's crew blows a loud horn. by the time the plane's sound detector receives the horn's sound, the plane has traveled a distance equal to one-third its altitude above the ocean. (a) if it takes the sound 1.92 s to reach the plane, determine the speed of the plane. (take the speed of sound to be 343 m/s.) /s (b) what is its altitude?

a) Speed of the plane= 108.47 (m/s)

b) Altitude of the plane: 624.77m

Explanation:

Using the speed of sound and the time it took to get to the plane we can determine the distance the sound traveled:

d=(343m/s) × (1.92s) = 658.56m

From the Pythagorean theorem, taking as the altitude and distance traveled two legs of a triangle and the situation traveled by the sound to the plane as the hypotenuse of this, we can establish the following equation:

(658.56m)²=( (1/3)×h)² + h²

Being h the altitude of the plane.

From here we can clear the altitude of the plane:

433701.27m² = (10/9)×h²

h²= 433701.27m² × (9/10)

h= (390331.14m²) ^ (1/2)

h= 624.77m

We know that the distance traveled by the plane until the sound is received is one third of the altitude, so this distance will be:

Distance= (1/3) × 624.77m= 208.25m

Considering the time in which the plane traveled this distance we can know the speed of it:

V= (208.25m) / (1.92s) = 108.47 (m/s)